The Wetterich flow equation is an exact differential
equation which must
be truncated, i.e. it must be projected to functions of few variables or even
onto some finite-dimensional sub-theory space. However as in nonperturbative
analysis [1]}, and discussed in introduction of this section the question of error estimate is very important and nontrivial in
functional renormalization. One way to estimate the error in FRG is to improve
the truncation in successive steps, i.e. to enlarge the sub-theory space
by including more and more running couplings. The difference in the flows
for different truncations gives a good estimate of the error. In addition,
one can use different regulator functions \(R_k\)  in a given (fixed) truncation and
determine the difference of the RG flows in the infrared for the respective
regulator choices. In this section, we adopt the simplest truncation, consisting in a restriction to the essential and marginal coupling with respect to the perturbative power counting (i.e. whose canonical dimension is upper or equal to zero). As mentioned before, such a truncation make sense as long as the anomalous dimension remains small, and a qualitative argument is the following. Let us define the anomalous dimension \(\eta :=\partial _s\ln (Z)\)  (see equation (REF ) below). In the vicinity of a fixed point, \(\eta \)  can reach to a non-zero value \(\eta _*\) . As a result, the effective propagator becomes:
\(\frac{Z^{-1}}{\vec{p}\,^2+(m_s^2/Z)}\approx \frac{e^{-\eta _* s}}{\vec{p}\,^2+m_*^2}\quad ,\) 
